Prove the sets A and B defined below are equal.

A = {(a, b) is a member of Z+ × Z+|a is a factor of b}

B is defined recursively by

Initial Step: (1, 1) is a member of B

Recursive Step: If (a, b) is a member of B and c is a member of Z+ then

(ac, bc) is a member of B and (a, bc) is a member of B